Rafael Jacinto Villanueva

Polytechnic University of Valencia | UPV · Institute for Multidisciplinary Mathematics (im2)

This paper introduces a methodology to build mathematical models based on evidence and data sets, considering data and model uncertainty. We study the evolution of obesity in the population, being obesity a consequence of the transmission of unhealthy lifestyle habits and behavioral patterns influenced by social networks (family, friends, peers, et...

Influenza and influenza-like illnesses (ILI) pose significant challenges to healthcare systems globally. Mathematical models play a crucial role in understanding their dynamics, calibrating them to specific scenarios, and making projections about their evolution over time. This study proposes a calibration process for three different but well-known...

This work presents and analyzes a numerical approach to efficiently solve the Liouville equation in the context of random ODEs using GPGPUs. Our method combines wavelet compression-based adaptive mesh refinement, Lagrangian particle methods, and radial basis function interpolation to create a versatile algorithm applicable in multiple dimensions. W...

Presentamos el estudio general de un problema clásico de vaciado de depósitos cuya forma es un sólido de revolución y que tiene un agujero circular en su base por donde se desaloja el líquido. Para ello, obtenemos la ecuación diferencial que describe la altura del líquido contenido en el depósito en cada instante temporal, h(t), así como el tiempo...

The International Conference on Mathematical Analysis and Applications in Science and Engineering –ICMA2SC’24 will take place at the beautiful city of Porto, Portugal, in June 20th-June 22nd 2024. This conference is dedicated to the memory of Prof JA Tenreiro Machado, who passed away in October 2021. Its aim is to bring together researchers in ev...

Vaccine efficacy and its quantification is a crucial concept for the proper design of public health vaccination policies. In this work we proposed a mathematical model to estimate the efficacy of the influenza vaccine in a real-word scenario. In particular, our model is a SEIR-type epidemiological model, which distinguishes vaccinated and unvaccina...

This paper deals with the probabilistic analysis of a class of compartmental models formulated via a system of linear differential equations with time‐dependent non‐homogeneous terms. For the sake of generality, we assume that initial conditions and rates between compartments are random variables with arbitrary distributions while the source terms...

We revisit a deterministic model for studying the dynamics of allelopathy. The model is formulated in terms of a non-homogeneous linear system of differential equations whose forcing or source term is a piecewise constant function (square wave). To account for the inherent uncertainties present in this natural phenomenon, we reformulate the model a...

p>The energy consumption of Artificial Intelligence (AI) systems has increased 300,000-fold from 2012 to now, and data centers running massive AI software produce up to 5-9% of global electricity demand and 2% of all CO2 emissions. Such an increase in energy consumption has been partially motivated by the strong development of new AI-specific archi...

p>The energy consumption of Artificial Intelligence (AI) systems has increased 300,000-fold from 2012 to now, and data centers running massive AI software produce up to 5-9% of global electricity demand and 2% of all CO2 emissions. Such an increase in energy consumption has been partially motivated by the strong development of new AI-specific archi...

Antibiotic resistance is one of the greatest public health threats today, mainly due to the non-rational use of antibiotics. Some of these microorganisms, such as Acinetobacter baumannii, which are especially problematic in hospitals, have rapidly developed resistance and only a few last-resort antibiotics, such as colistin, are effective against t...

In the real world, multiple dynamic biological phenomena present an intrinsic randomness due to their nature. One of the most common ways of modeling them is to use random differential or random difference equations, whose parameters are considered as random variables. However, since these are complex models, independence between these parameters i...

Candida Auris is a pathogen that can express multiple virulence factors and is considered a significant menace to the Intensive Care Unit environment. In this work, we propose to model its growth with a computationally randomized Fisher Kolmogorov–Petrovsky–Piskunov partial differential equation. We calibrate the model using in vitro growth data an...

The first probability density function associated with the solution of a stochastic process defined by differential equations can often be obtained by the Random Variable Transformation (RVT) method. The application of this method allows us to obtain, as a solution, a function which depends on random inputs (parametric-type stochastic process). How...

We propose a new mathematical model, based on a differential equation, to describe the dynamics in the number of Spotify users. The model takes into account that the adoption of new technologies is determined by complex social factors whose nature is random. This aims us to treat that the peer-pressure and advertisement rates as random variables in...

Breast cancer is one of the most common cancers globally, affecting mainly women. To determine the stage of breast cancer, one of the “key pieces of information” is the size of the tumor and if it has grown in nearby areas. Knowing the evolution of the tumor size helps doctors when to start treatments, which to apply, the number of times they are n...

In this contribution we perform a full probabilistic solution of a random generalized logistic initial value problem whose parameters involve both continuous and discrete uncertainties. To do it, the first probability density function of the solution stochastic process is computed using the Random Variable Transformation method and taking advantage...

We extend the study of the random Hermite second-order ordinary differential equation to the fractional setting. We first construct a random generalized power series that solves the equation in the mean square sense under mild hypotheses on the random inputs (coefficients and initial conditions). From this representation of the solution, which is a...

This contribution aims at studying a general class of random differential equations with Dirac-delta impulse terms at a finite number of time instants. Our approach directly addresses calculating the so-called first probability density function, from which all the relevant statistical information about the solution, a stochastic process, can be ext...

https://www.ajman.ac.ae/en/icfda2022//

Objective: To evaluate the cost-effectiveness of infant universal vaccination against hepatitis A in Spain. Method: Using a dynamic model and decision tree model, a cost-effectiveness analysis was performed to compare three vaccination strategies against hepatitis A: non-vaccination strategy versus universal childhood vaccination of hepatitis A...

In this contribution, we rigorously construct a pathwise solution to a general scalar random differential equation with state-dependent Dirac-delta impulse terms at a finite number of time instants. Furthermore, we obtain the first probability density function of the solution by combining two main results, firstly, the Liouville-Gibbs equation betw...

An open problem in diabetes clinical practice is determining where and how much insulin should be administered to a person with diabetes (PwD) and how many carbohydrates they should eat to maintain blood glucose levels at healthy safe levels. Here, we propose the use of a minimal model describing the glucose dynamics of PwD. Using glucose Pwd's dat...

Time-continuous dynamical systems governed by ordinary differential equations form a large and influential family of mathematical models used in physics, chemistry, biology, and engineering. When analyzing and simulating real-world phenomena, uncertainty in the model itself and the tolerance errors in measurement devices must be considered. This pa...

In this chapter, we model breast tumor’s growth with the logistic discrete Pielou model. Data of tumor volume is retrieved from the literature. We assign probability density functions (PDF) to the data and their uncertainty using the principle of maximum entropy. Then, we propose a computational technique, probabilistic calibration (PC), to calibra...

A number of relevant models in Classical Mechanics are formulated by means of the differential equation y′′(t)+Atβy(t)=0. In this paper, we improve the results recently established for a randomized reformulation of this model that includes a generalized derivative. The stochastic analysis permits solving that generalized model by computing reliable...

This paper deals with random fractional differential equations of the form, CD0+αX(t)+AX˙(t)+BX(t)=0, t>0, with initial conditions, X(0)=C0 and X˙(0)=C1, where CD0+αX(t) stands for the Caputo fractional derivative of X(t). We consider the case that the fractional differentiation order is 1<α<2. For the sake of generality, we further assume that C0,...

The so-called logistic model with harvesting, p′(t)=rp(t)(1−p(t)K)−c(t)p(t), p(t0)=p0, is a classical ecological model that has been extensively studied and applied in the deterministic setting. It has also been studied, to some extent, in the stochastic framework using the Itô Calculus by formulating a Stochastic Differential Equation whose uncert...

Objective The COVID-19 pandemic has threatened to collapse hospital and ICU services, and it has affected the care programs for non-COVID patients. The objective was to develop a mathematical model designed to optimize predictions related to the need for hospitalization and ICU admission by COVID-19 patients. Design Prospective study. Setting Pro...

We study a full randomization of the complete linear differential equation subject to an infinite train of Dirac's delta functions applied at different time instants. The initial condition and coefficients of the differential equation are assumed to be absolutely continuous random variables, while the external or forcing term is a stochastic proces...

We study, from a probabilistic standpoint, first-order impulsive linear differential equations, where all its parameters (initial condition and coefficients) are absolutely continuous random variables with a joint probability density function. We assume an infinite train of Dirac delta impulse applications at given time instants to control the mode...

An epidemiological model is proposed to study the transmission dynamics of the herpes virus type 2, a sexually transmitted infectious disease. This model considers two states, susceptible and infected, divides the population into sexes, assumes only heterosexual contacts and includes different transmission rates depending on whether the transmissio...

An important class of non-homogeneous first-order linear random differential equations subject to an infinite sequence of square impulses with random intensity is studied. In applications, these equations are useful to model the dynamics of a population with periodic harvesting and migration under uncertainties. The solution is explicitly obtained...

e18663 Background: The COVID-19 pandemic has threatened to collapse hospital and Intensive Care Unit (ICU) services, and it seems to limit the care of oncologic patients. The objective was to develop a mathematical model designed to predict the hospitalization and ICU admission demands due to COVID-19 to forecast the availability of hospital resour...

Mathematical models have been remarkable tools for knowing in advance the appropriate time to enforce population restrictions and distribute hospital resources. Here, we present a mathematical Susceptible-Exposed-Infectious-Recovered (SEIR) model to study the transmission dynamics of COVID-19 in Granada, Spain, taking into account the uncertainty o...

Cervical cancer is the fourth most common malignancy in women worldwide, although it is preventable with prophylactic HPV vaccination. HPV transmission-dynamic models can predict the potential for the global elimination of cervical cancer. The random network model is a new approach that allows individuals to be followed, and to implement a given va...

Abstract. In this paper we propose a stochastic mathematical model with distributed delay in order to describe the transmission dynamics of cocaine consumption in Spain. We investigate conditions to guarantee the stability in probability of the equilibrium points under stochastic perturbations via the white noise processes. The results are applied...

The administration of vaccines against the coronavirus disease 2019 (COVID-19) started in early December of 2020. Currently, there are only a few approved vaccines, each with different efficacies and mechanisms of action. Moreover, vaccination programs in different regions may vary due to differences in implementation, for instance, simply the avai...

Several SARS-CoV-2 variants have emerged around the world, and the appearance of other variants depends on many factors. These new variants might have different characteristics that can affect the transmissibility and death rate. The administration of vaccines against the coronavirus disease 2019 (COVID-19) started in early December of 2020 and in...

The Baranyi–Roberts model describes the dynamics of the volumetric densities of two interacting cell populations. We randomize this model by considering that the initial conditions are random variables whose distributions are determined by using sample data and the principle of maximum entropy. Subsequenly, we obtain the Liouville–Gibbs partial dif...

Cervical cancer is the fourth most common malignancy in women worldwide, although it is preventable with prophylactic HPV vaccination. HPV transmission-dynamic models can predict the potential for global elimination of cervical cancer. The random network model is a new approach that allows individuals to be followed, and to implement a given vaccin...

We provide a full stochastic description, via the first probability density function, of the solution of linear-quadratic logistic-type differential equation whose parameters involve both continuous and discrete random variables with arbitrary distributions. For the sake of generality, the initial condition is assumed to be a random variable too. W...

S everal SARS-CoV-2 variants have emerged around the world and the appearance of other variants depends on many factors. These new variants might have different characteristics that can affect the transmissibility and death rate. The administration of vaccines against the coronavirus disease 2019 (COVID-19) started in early December of 2020 and in...

Resumen Objetivo: La pandemia de la COVID-19 ha supuesto una amenaza de colapso de los servicios hospitalarios y de UCI, y una reducción de la dinámica asistencial de pacientes afectados por otras patologías. El objetivo fue desarrollar un modelo matemático diseñado para optimizar las predicciones relacionadas con las necesidades de hospitalización...

The administration of vaccines against the coronavirus disease 2019 (COVID-19) just started in early December of 2020. Currently, there are only a few approved vaccines, each with different efficacies and mechanisms of action. Moreover, vaccination programs in different regions may vary due to differences in implementation, for instance, simply the...

In this paper, we consider a random network model for sexual contacts in a population developed from real statistical data in order to assess vaccination policies against sexually transmitted diseases (STDs). The model is constructed by imposing a constraint requiring that individuals of a given sex, in a given age group, would have an average conn...

A major challenge in human papillomavirus (HPV) vaccine programs is the universal gender-neutral recommendation, as well as estimation of its long-term effect. The objective of this study is to predict the added benefit of male vaccination, especially in men who have sex with men (MSM), and to analyze the impact of the program on society. We propos...

In this paper we propose a technique to estimate the effectiveness of the influenza vaccine. The effectiveness of the vaccine is estimated every year, when the influenza season has finished, analyzing samples of a high number of patients in the emergency departments of the hospitals, and this makes it very expensive.

Random fractional differential equations are useful mathematical tools to model problems involving memory effects and uncertainties. In this contribution, we present some results, which extent their deterministic counterpart, to fractional differential equations whose initial conditions and coefficients are random variables and/or stochastic proces...

Taking into account the public health importance of the human papillomavirus (HPV) control in the future, it is mandatory to assess the effect of the vaccination campaigns on the control of HPV spread and the associated diseases using reliable mathematical models. We propose a computational random network model with the aim of studying the transmis...

Objective. The COVID-19 pandemic has threatened to collapse hospital and ICU services, and it has affected the care programs for non-COVID patients. The objective was to develop a mathematical model designed to optimize predictions related to the need for hospitalization and ICU admission by COVID-19 patients. Design. Prospective study. Setting. Pr...

In this contribution, we revisit the Liouville-Gibbs theorem for dynamical systems. This theorem states that a partial differential equation that is satisfied by the probability density function of the solution stochastic process of an initial value problem with uncertainties in its initial condition, forcing term and coefficients. We show its key...

The coronavirus disease 2019 (COVID-19) that emerged in China at the end of 2019 has spread worldwide. In this article, we present a mathematical SEIR model focused on analysing the transmission dynamics of COVID-19, the patients circulating in the hospitals and evaluating the effects of health policies and vaccination on the control of the pandemi...

We consider a randomized discrete logistic equation to describe the dynamics of breast tumor volume. We propose a method, that takes advantage of the principle of maximum entropy, to assign reliable distributions to model inputs (initial condition and coefficients) and sample data, respectively. Since the distributions of coefficients depend on cer...

In spite of its simple formulation via a nonlinear differential equation, the Gompertz model has been widely applied to describe the dynamics of biological and biophysical parts of complex systems (growth of living organisms, number of bacteria, volume of infected cells, etc.). Its parameters or coefficients and the initial condition represent biol...

It seems that we are far from controlling COVID-19 pandemics, and, consequently, returning to a fully normal life. Until an effective vaccine is found, safety measures as the use of face masks, social distancing, washing hands regularly, etc., have to be taken. Also, the use of appropriate antivirals in order to alleviate the symptoms, to control t...

A fractional forward Euler-like method is developed to solve initial value problems with uncertainties formulated via the Caputo fractional derivative. The analysis is conducted by using the so-called random mean square calculus. Under mild conditions on the data, the mean square convergence of the numerical method is proved. This type of stochasti...

The particle swarm optimization algorithm is based on swarm behaviour and has achieved important results in different applications. However, it is not exempt from stagnation in local optima and has a tendency to converge prematurely. Novelty Search is a concept that has appeared recently in different fields of computational intelligence. It aims to...

Grammatical Swarm is a search and optimization algorithm that belongs to the more general Grammatical Evolution family, which works with a set of solutions called individuals or particles. It uses the Particle Swarm Optimization algorithm as the search engine in the evolution of solutions. In this paper, we present a Grammatical Swarm algorithm for...

On advanced stages of the disease, diabetic patients have to inject insulin doses to maintain blood glucose levels inside of a healthy range. The decision of how much insulin inject implies somehow to predict the level of glucose they will have after a certain time. Due to the sudden changes in the glucose levels, their estimation is a very difficu...

In this paper, we retrieve data about the frequent users of electronic commerce during the period 2011–2016 from the Spanish National Institute of Statistics. These data, coming from surveys, have intrinsic uncertainty that we describe using appropriate random variables. Then, we propose a stochastic model to study the dynamics of frequent users of...

This paper describes the development and the conclusion of the meeting the professors of the Faculty of Business Administration in charge of the “point of control” subjects of the soft skill “Problem Analysis and Solving” (CT3) in the first and second level, held May 6th, 2019. The professors share their experience in implementing assessment method...